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Grain refinement of undercooled single-phase Fe70Co30 alloys
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Physica B 387 (2007) 151–155 www.elsevier.com/locate/physb
Grain refinement of undercooled single-phase Fe70Co30 alloys Ning Liu, Feng Liu, Gencang Yang, Yuzeng Chen, Da Chen, Changlin Yang, Yaohe Zhou State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an Shaanxi 710072, PR China Received 26 October 2005; received in revised form 29 March 2006; accepted 29 March 2006
Abstract The grain refinement mechanism of undercooled single-phase Fe70Co30 alloy was investigated. With increasing the initial melt undercooling (DT), the first grain refinement occurs within 22 KoDTo87 K, and the second one if DT4183 K. Applying a dendrite break-up model (i.e. on the basis of morphological instability) in combination with the BCT model calculation, a theoretical description for the observed grain refinements is given. Both grain refinements are concluded to be caused by dendrite remelting. Good agreement between theoretical expectation and experimental result was found for the second grain refinement. As for the first grain refinement, only the initiating undercooling (i.e. DT ¼ 22 K) can be predicted using the above model, whereas large deviation remains for the ending undercooling (i.e. DT ¼ 87 K). This can be ascribed to the fact that the effect of solutal diffusion was deduced to be negligible for DT425 K in BCT model calculation. r 2006 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 61.66.Dk Keywords: Grain refinement; Single-phase alloy; Undercooling; Fe70Co30 alloy
1. Introduction Grain refinement in undercooled melts was first found in pure nickel by Walker [1] in 1956, in which the grain size abruptly decreased by about 1–2 orders of magnitude if the initial melt undercooling, DT prior to nucleation exceeds a critical value DT*. Since the occurrence of the grain size reduction was accompanied by the emission of sound waves, he concluded that the refinement resulted from the copious homogeneous nucleation induced by the pressure pulse generated from the collapse of shrinkage cavities. However, Jackson, Flemings and coworkers [2,3] suggested that the fine-grained structure of the Ni–Cu alloy should be attributed to the dendrite remelting due to recalescence. Furthermore, Mullis and Cochrane [4] have carried out a stability analysis of dendrite growth based on a marginal stability model. They predicted that growth should be unstable at both low and high undercooling, and they associated the occurrence of grain refinement with this instability. Willnecker et al. [5] demonstrated that grain Corresponding author. Tel.: +86 29 88460374; fax: +86 29 88492374.
E-mail address: [email protected] (F. Liu). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.03.101
refinement in Ni–Cu or Ni–Cu–B alloys might be caused by a discontinuous change of growth velocity when the alloys are undercooled up to the critical undercoolings, at which the grain sizes drop abruptly by more than two orders of magnitude in both alloys. Recently, a transition from primary solidification of stable FCC phase to primary solidification of metastable BCC phase was found in undercooled Fe70Co30 alloy when undercooling exceeds a critical value of about 60–80 K below the equilibrium liquidus temperature [6]. Unfortunately, present experiment result is dissimilar with above outcome. It was found that the undercooled Fe70Co30 alloy solidifies as single phase under certain critical undercooling in this paper. Whether the grain refinement mechanism of Fe-30 at% Co alloy is analogous to that of some singlephase alloys, such as Ni–Cu [2,3,5,7,8], and DD3 superalloy [9] deserves further investigation of the corresponding structure evolution. 2. Experiment High-purity elements of iron (Fe) and cobalt (Co) better than 99.95 wt% were alloyed in situ to form 5 g samples.
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Bulks with the composition of Fe-30 at% Co alloys were prepared in quartz tubes in a high-frequency apparatus under the protection of B2O3 glass slag so as to denucleate the alloy by reaction, adsorption, and passivation of the foreign catalytic site. Each sample was melted, superheated and solidified several times, in order to obtain large undercoolings. After the high-frequency power source was turned off, the alloy sample was cooled spontaneously, while thermal behavior of samples was monitored by an infrared pyrometer with an absolute accuracy, relative accuracy, and response time of less than 10, 3 K, and 5 ms [10]. The cooling curve was calibrated with a standard PtRh30–PtRh6 thermal couple, which was encapsulated in a silica tube and then immersed into the melt in the identical condition. The melting temperature and the undercoolings of the alloy in the cooling curves could be read as compared to the absolute temperature recorded by the standard thermal couple. Only one recalescence was observed during experiment because of limitation of experimental condition, but other investigators [6] found two recalescences in their work. Note that no chemical reactions could occur between the melt and the glass slag, so the composition of the assolidified specimens was taken to be the same as the original one. Each sample was polished, and then etched with 3 wt% nitric acid solution diluted with alcohol. The microstructures subjected to various undercoolings were observed using an optical microscope.
Fig. 1. Grain size as a function of undercooling DT.
3. Experimental results Single-phase solidification of undercooled Fe-30 at%Co melt can be described as follows. Once the melt is undercooled to the nucleation point, dendrites form and propagate rapidly through the volume of the melt, and then the rapid release of heat of fusion during dendrite growth leads to rapid recalescence, thus resulting in remelting of the dendrite network. Thereafter, the remaining interdendritic liquid starts to solidify onto the dendritic network at low melt undercooling in post-recalescence. Here, two grain refinements were observed in the undercooling range of 0–203 K, as compatible with phenomenon observed in other single phase alloys, such as Ni–Cu [7,8] and DD3 superalloy [9]. Using several characteristic undercooling: DT*1 ¼ 22 K, DT*2 ¼ 87 K, DT*3 ¼ 97 K, DT*4 ¼ 173 K, DT*5 ¼ 183 K, DT*6 ¼ 203 K, the microstructure of the as-solidified Fe70Co30 alloy melt can be classified as follows. If DToDT*1, coarse dendrites result, but they are substituted by refined granular crystals within DT*1oDToDT*2; see Figs. 1 and 2a–c. Further increasing undercooling to DT*3 changes the above granular crystals into directional fine dendrites, whose first arm spacing become finer with increasing DT up to DT*4; see Figs. 2d and e. For DT*5oDToDT*6, the second grain refinement occurs and granular crystals result; see Fig. 2f. Due to the formation of metastable phase after DT*6, an interesting grain coarsening
Fig. 2. Typical microstructures Fe70Co30 alloy with undercooling of (a) 0 K, (b) 22 K, (c) 87 K, (d) 97 K, (e) 154 K, (f) 183 K, (g) 203 K, (h) 245 K.
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was found [11], see Figs. 2g and h. In this paper, we aim to investigate the above two grain refinements. A detailed description for the grain coarsening is available in Ref. [11]. 4. Discussion 4.1. The first grain refinement As described in Section 3, coarse dendrites form by introducing a small undercooling. However, the heat released due to recalescence increases the temperature of the melt up to even higher than the melting point. This phenomenon was also observed in this case. Obviously, the coarse dendrites are attacked by the serious remelting and thus break up into refined granular crystals; see Fig. 2b. In combination with the previous research about grain refinement occurring in Ni–Cu [7,8] and DD3 Superalloy [9], the grain refinement of single-phase alloys at small undercoolings should be caused by remelting of the primary dendrites; see Section 4.3.
the plateau duration Dtpl for the inter-dendritic melt to be completely solidified after recalescence. Grain refinement occurs only if Dtpl4Dtbu [14,15]. Such critical undercoolings for the onset of grain refinement arise because Dtbu and Dtpl depend, in different ways, on the undercooling prior to nucleation [16]. Applying this model in Ni–Cu alloy [7], a good quantitative agreement was obtained between the model prediction and the experimental observation. For example, the model predicts the existence of four grain refinement transitions, three of which were observed experimentally. Here the grain refinements in as-solidified Fe–Co alloys were interpreted using the above model. The basic underlying assumption of the above model is that remelting of the dendrite trunks is driven both by capillary forces and by the supersaturation inside the trunk, which becomes important at high undercooling [17]. The fragmentation can be evaluated by adopting a parameter S, the so-called dimensionless measurement of the relative contribution from the two aforementioned driving forces [17],
4.2. The second grain refinement S¼ So far, two kinds of mechanisms for the second grain refinement occurring at high undercooling are favored. The first one is dendrite remelting of the primary dendrites [3], and the second one is recrystallization occurring in the dendrite fragments. As for recrystallization mechanism, Liu et al. [9] deemed that the second grain refinement in DD3 superalloy can be attributed to large stresses originating from lattice deformation and fluid flow induced by solidification shrinkage due to rapid solidification, which results in dendrite distortion, disintegration and recrystallization. Analogously, Li et al. [8] considered that the second grain refinement in Ni–Cu alloy results from the stress caused by the impeded solidification contraction in rapid solidification, which leads to fragmentation and recrystallization of the dendrites. As a fact, dislocations and twins that are indications of recrystallized microstructure were not found in the as-solidified structures of Fe–Co alloy. Furthermore, the average grain diameter was comparable to the dendrite trunk radius, i.e. the dendrite side-branch spacing, so the second grain refinement possibly results from remelting of the primary dendrites rather than recrystallization. 4.3. Comparison with a dendrite break-up model Based on previous work by Jackson et al. [12], a model was proposed for dendrite fragmentation, which is based on the morphological instability of a solid cylinder embedded in its melt leading to a fragmentation of the cylinder into spheres [13]. The driving force for this process is the reduction of the solid–liquid interfacial area. According to this model, the critical transitional undercooling could be determined by comparing two times: the time for dendrite break-up by Rayleigh instability Dtbu and
153
Gc R Ds R , C 0 ð1 kE Þ Dl d c0
(1)
where Gc is the concentration gradient which is negative because the concentration decreases outward from the trunk axis, and d c0 , the chemical capillary length, can be expressed as d c0
G . jml jð1 kE Þc0
(2)
According to Ref. [17], fragmentation is dominated by surface tension and supersaturation inside the trunk, for S51 and Sb1, respectively. On this basis, the prediction in this case for Dtbu (for S51) can be expressed as jml jc0 ð1 kE Þ Dl 3 RðDT Þ3 , (3) 1þ Dtbu ðDTÞ 2 d 0 DT DH f =C p DT where Dl and Ds denote the solute diffusivities in the liquid and solid phase, respectively, DT the thermal diffusivity in the liquid, ml the equilibrium liquidus slope, kE the equilibrium partition coefficient, DHf the heat of fusion, Cp the specific heat at constant pressure, c0 the solute concentration, and d0 ( ¼ Cp/DHf) the capillary length with G the Gibbs–Thomson coefficient. According to Schwarz’s model [18], the trunk radius R(DT) is correlated to the dendrite tip radius, Rtip(DT), via a proportionality constant, z ¼ RðDTÞ=Rtip ðDTÞ 20. This constant is determined by taking the ratio of the trunk radius, measured from micrographs of solidified samples, to the calculated tip radius at the same undercooling. Applying the physical parameter data of Fe70Co30 alloy (see Table 1), the theoretical dendrite tip radius R(DT), as a function of undercooling, was calculated using BCT model [19]. The calculated Dtbu and Dtpl as a function of undercooling are shown in Fig. 3. Three intersection points between Dtbu and Dtpl were observed, indicating that two
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Table 1 Materials parameters of Fe70Co30 used in the calculation of the break-up time Parameter
Dimension
Value
Heat of fusion (DHf) Specific heat (Cp) Liquidus temperature (Tl) Liquidus slope (ml) Diffusion coefficient (Dc) Thermal diffusivity (DT) Equilibrium partition coeffcient (kE) Gibbs–Thomson coefficient (G)
J/mol J/mol K K K/at% m2/s m2/s
15 608 38.4 1765 1.2 4.4 109 2.4 106 0.73 3.7 107
km
Fig. 4. Undercooling contributions vs initial undercooling T.
Fig. 3. Calculated dendrite break-up time Dtbu (thick solid line) and plateau time Dtpl (thin solid line) as a function of undercooling.
grain refinements occur, i.e. the first one occurs within 20 KoDTexpo30 K, and the second one if DTexp4175 K. Basically speaking, this is compatible with the theoretical expectation, i.e. two grain refinements occur at both low and high undercoolings. For the second grain refinement, good agreement was obtained between the theoretical expectation and the experimental result, i.e. DT exp ¼ 175 KDT 5 ¼ 183 K. For the first grain refinement, however, only the initiating undercooling can be predicted using the above model, i.e. DT exp ¼ 20 KDT 1 ¼ 22 K, whereas large deviation remains for the ending undercooling (i.e. DT exp ¼ 30 K DT 2 ¼ 87 K). According to the BCT model [19], the total undercooling at the dendrite tip consists of four contributions, DT ¼ DT l þ DT c þ DT r þ DT k ,
(4)
where DTt, DTc, DTr, and DTk are the thermal, solutal, curvature, and kinetic undercooling, respectively. With increasing DT, the variation of the relative contributions of Tt and DTc to DT reflected that solutal diffusion-controlled growth may give way to thermal diffusion-controlled
growth. As shown in Fig. 4, solutal diffusion predominates if DTo20 K, but it is progressively replaced by thermal diffusion with DT, i.e. the cross-point of DTt and DTc (DT ¼ 25 K) corresponds to the transition from solutal diffusion-controlled growth to thermal diffusion-controlled growth, see Fig. 4. It is then concluded that the effect of solutal diffusion becomes negligible after DT ¼ 25 K according to the BCT model calculation. From Eq. (3), Dtbu is dependent on Rtip(DT) calculated using BCT model, so the regime for the first grain refinement, 20 KoDTexpo30 K (see Fig. 3), was deduced, as compatible with the above conclusion from Fig. 4. As shown in Fig. 1, however, the first granular crystals hold within 22 KoDTo87 K, which implies that the effect of solutal diffusion is still inevitable wherein. So the conclusion that the effect of solutal diffusion becomes negligible after DT ¼ 25 K drawn from BCT model calculation (see Fig. 4) is not physically realistic. On this basis, further considering the effect of solutal diffusion must enlarge the regime for the first grain refinement (see Fig. 3). This is why large deviation remains for the ending undercooling (i.e. DT exp ¼ 30 K DT 2 ¼ 87 K) for the first grain refinement. Unfortunately, only a qualitative interpretation is given here. Anyway, a quantitative explanation is essential for a more detailed investigation on the occurring phenomenon. 5. Conclusion Analogous to other single-phase alloys such as Ni–Cu and DD3 superalloy, two grain refinements were observed in the as-solidified Fe70Co30 alloy melt subjected to undercoolings below a critical value. The first grain refinement occurs within 22 KoDTo87 K, and the second one if DT4183 K. Applying a dendrite break-up model (i.e. on the basis of morphological instability) in combination
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with the BCT model calculation, a theoretical description for the observed grain refinements was given. Both grain refinements are concluded to be caused by dendrite remelting. Good agreement between theoretical expectation and experimental result was found for the second grain refinement, i.e. DT exp ¼ 175 KDT 5 ¼ 183 K. As for the first grain refinement, only the initiating undercooling can be predicted using the above model, i.e. DT exp ¼ 20 KDT 1 ¼ 2 K, whereas large deviation remains for the ending undercooling, i.e. DT exp ¼ 30 K DT 2 ¼ 87 K. This can be ascribed to the fact that the effect of solutal diffusion was deduced to be negligible for DT425 K in BCT model calculation. Acknowledgments The authors are grateful to the financial support of the Natural Science Foundation of China (Grant nos. 50395103 and 50501020). References [1] J.L. Walker, in: G.R.S. Pierre (Ed.), Physical of Process Metallurgy, Part 2, AIME, Interscience, New York, 1961, p. 845. [2] K.A. Jackson, J.D. Hunt, D.R. Uhlmann, J. Mater. Sci. Lett. 245 (1969) 407.
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[3] T.Z. Kattamis, M.C. Flemings, Trans. TMS-AIME 236 (1966) 1523. [4] A.M. Mullis, R.F. Cochrane, J. Appl. Phys. 82 (1997) 3783. [5] R. Willnecker, D.M. Herlach, B. Feuerbacher, Appl. Phys. Lett. 56 (1990) 324. [6] R. Hermann, W. Lo¨ser, G. Lindenkreuz, A. Diefenbach, W. Zahnow, W. Dreier, Th. Volkmann, D. Herlach, Mater. Sci. Eng. A 375–377 (2004) 507. [7] D.M. Herlach, K. Eckler, A. Karma, M. Schwarz, Mater. Sci. Eng. A 304–306 (2001) 20. [8] J.F. Li, Y.C. Liu, Y.L. Lu, G.C. Yang, Y.H. Zhou, J. Cryst. Growth 192 (1998) 462. [9] L. Feng, Y. Gencang, G. Xuefeng, Mater. Sci. Eng. A 311 (2001) 54. [10] J. Li, G. Yang, Y. Zhou, Mater. Res. Bull. 33 (1998) 141. [11] N. Liu, G. Yang, F. Liu, Y. Chen, Y. Zhou. Mater. Charact., in press [12] K.A. Jackson, J.D. Hunt, D.R. Uhlmann, T.P. Seward, Trans. TMS AIME 236 (1966) 149. [13] M. Schwarz, A. Karma, K. Eckler, D.M. Herlach, Phys. Rev. Lett. 73 (1994) 1380. [14] A. Karma, Int. J. Non-equilib. Proc. 11 (1998) 201. [15] A.F. Norman, K. Eckler, A. Zambon, F. Gae`rtner, S.A. Moir, E. Ramous, D.M. Herlach, A.L. Greer, Acta mater 46 (10) (1998) 3355–3370. [16] K. Eckler, M. Schwarz, A. Karma, D.M. Herlach, Mater. Sci. Forum 45 (1996) 215. [17] A. Karma, Int. J. Non-Equilib. Process. 11 (1998) 201. [18] M. Schwarz, A. Karma, K. Eckler, D.M. Herlach, Phys. Rev. Lett. 73 (1994) 1380. [19] W.J. Boettinger, S.R. Coriell, R. Trivedi, in: R. Mehrabian, P.A. Parrish (Eds.), Rapid Solidification Processing Principles and Technologies IV, Claitors, Baton Rouge LA, 1988, p. 13.
Physica B 387 (2007) 151–155 www.elsevier.com/locate/physb
Grain refinement of undercooled single-phase Fe70Co30 alloys Ning Liu, Feng Liu, Gencang Yang, Yuzeng Chen, Da Chen, Changlin Yang, Yaohe Zhou State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an Shaanxi 710072, PR China Received 26 October 2005; received in revised form 29 March 2006; accepted 29 March 2006
Abstract The grain refinement mechanism of undercooled single-phase Fe70Co30 alloy was investigated. With increasing the initial melt undercooling (DT), the first grain refinement occurs within 22 KoDTo87 K, and the second one if DT4183 K. Applying a dendrite break-up model (i.e. on the basis of morphological instability) in combination with the BCT model calculation, a theoretical description for the observed grain refinements is given. Both grain refinements are concluded to be caused by dendrite remelting. Good agreement between theoretical expectation and experimental result was found for the second grain refinement. As for the first grain refinement, only the initiating undercooling (i.e. DT ¼ 22 K) can be predicted using the above model, whereas large deviation remains for the ending undercooling (i.e. DT ¼ 87 K). This can be ascribed to the fact that the effect of solutal diffusion was deduced to be negligible for DT425 K in BCT model calculation. r 2006 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 61.66.Dk Keywords: Grain refinement; Single-phase alloy; Undercooling; Fe70Co30 alloy
1. Introduction Grain refinement in undercooled melts was first found in pure nickel by Walker [1] in 1956, in which the grain size abruptly decreased by about 1–2 orders of magnitude if the initial melt undercooling, DT prior to nucleation exceeds a critical value DT*. Since the occurrence of the grain size reduction was accompanied by the emission of sound waves, he concluded that the refinement resulted from the copious homogeneous nucleation induced by the pressure pulse generated from the collapse of shrinkage cavities. However, Jackson, Flemings and coworkers [2,3] suggested that the fine-grained structure of the Ni–Cu alloy should be attributed to the dendrite remelting due to recalescence. Furthermore, Mullis and Cochrane [4] have carried out a stability analysis of dendrite growth based on a marginal stability model. They predicted that growth should be unstable at both low and high undercooling, and they associated the occurrence of grain refinement with this instability. Willnecker et al. [5] demonstrated that grain Corresponding author. Tel.: +86 29 88460374; fax: +86 29 88492374.
E-mail address: [email protected] (F. Liu). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.03.101
refinement in Ni–Cu or Ni–Cu–B alloys might be caused by a discontinuous change of growth velocity when the alloys are undercooled up to the critical undercoolings, at which the grain sizes drop abruptly by more than two orders of magnitude in both alloys. Recently, a transition from primary solidification of stable FCC phase to primary solidification of metastable BCC phase was found in undercooled Fe70Co30 alloy when undercooling exceeds a critical value of about 60–80 K below the equilibrium liquidus temperature [6]. Unfortunately, present experiment result is dissimilar with above outcome. It was found that the undercooled Fe70Co30 alloy solidifies as single phase under certain critical undercooling in this paper. Whether the grain refinement mechanism of Fe-30 at% Co alloy is analogous to that of some singlephase alloys, such as Ni–Cu [2,3,5,7,8], and DD3 superalloy [9] deserves further investigation of the corresponding structure evolution. 2. Experiment High-purity elements of iron (Fe) and cobalt (Co) better than 99.95 wt% were alloyed in situ to form 5 g samples.
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Bulks with the composition of Fe-30 at% Co alloys were prepared in quartz tubes in a high-frequency apparatus under the protection of B2O3 glass slag so as to denucleate the alloy by reaction, adsorption, and passivation of the foreign catalytic site. Each sample was melted, superheated and solidified several times, in order to obtain large undercoolings. After the high-frequency power source was turned off, the alloy sample was cooled spontaneously, while thermal behavior of samples was monitored by an infrared pyrometer with an absolute accuracy, relative accuracy, and response time of less than 10, 3 K, and 5 ms [10]. The cooling curve was calibrated with a standard PtRh30–PtRh6 thermal couple, which was encapsulated in a silica tube and then immersed into the melt in the identical condition. The melting temperature and the undercoolings of the alloy in the cooling curves could be read as compared to the absolute temperature recorded by the standard thermal couple. Only one recalescence was observed during experiment because of limitation of experimental condition, but other investigators [6] found two recalescences in their work. Note that no chemical reactions could occur between the melt and the glass slag, so the composition of the assolidified specimens was taken to be the same as the original one. Each sample was polished, and then etched with 3 wt% nitric acid solution diluted with alcohol. The microstructures subjected to various undercoolings were observed using an optical microscope.
Fig. 1. Grain size as a function of undercooling DT.
3. Experimental results Single-phase solidification of undercooled Fe-30 at%Co melt can be described as follows. Once the melt is undercooled to the nucleation point, dendrites form and propagate rapidly through the volume of the melt, and then the rapid release of heat of fusion during dendrite growth leads to rapid recalescence, thus resulting in remelting of the dendrite network. Thereafter, the remaining interdendritic liquid starts to solidify onto the dendritic network at low melt undercooling in post-recalescence. Here, two grain refinements were observed in the undercooling range of 0–203 K, as compatible with phenomenon observed in other single phase alloys, such as Ni–Cu [7,8] and DD3 superalloy [9]. Using several characteristic undercooling: DT*1 ¼ 22 K, DT*2 ¼ 87 K, DT*3 ¼ 97 K, DT*4 ¼ 173 K, DT*5 ¼ 183 K, DT*6 ¼ 203 K, the microstructure of the as-solidified Fe70Co30 alloy melt can be classified as follows. If DToDT*1, coarse dendrites result, but they are substituted by refined granular crystals within DT*1oDToDT*2; see Figs. 1 and 2a–c. Further increasing undercooling to DT*3 changes the above granular crystals into directional fine dendrites, whose first arm spacing become finer with increasing DT up to DT*4; see Figs. 2d and e. For DT*5oDToDT*6, the second grain refinement occurs and granular crystals result; see Fig. 2f. Due to the formation of metastable phase after DT*6, an interesting grain coarsening
Fig. 2. Typical microstructures Fe70Co30 alloy with undercooling of (a) 0 K, (b) 22 K, (c) 87 K, (d) 97 K, (e) 154 K, (f) 183 K, (g) 203 K, (h) 245 K.
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was found [11], see Figs. 2g and h. In this paper, we aim to investigate the above two grain refinements. A detailed description for the grain coarsening is available in Ref. [11]. 4. Discussion 4.1. The first grain refinement As described in Section 3, coarse dendrites form by introducing a small undercooling. However, the heat released due to recalescence increases the temperature of the melt up to even higher than the melting point. This phenomenon was also observed in this case. Obviously, the coarse dendrites are attacked by the serious remelting and thus break up into refined granular crystals; see Fig. 2b. In combination with the previous research about grain refinement occurring in Ni–Cu [7,8] and DD3 Superalloy [9], the grain refinement of single-phase alloys at small undercoolings should be caused by remelting of the primary dendrites; see Section 4.3.
the plateau duration Dtpl for the inter-dendritic melt to be completely solidified after recalescence. Grain refinement occurs only if Dtpl4Dtbu [14,15]. Such critical undercoolings for the onset of grain refinement arise because Dtbu and Dtpl depend, in different ways, on the undercooling prior to nucleation [16]. Applying this model in Ni–Cu alloy [7], a good quantitative agreement was obtained between the model prediction and the experimental observation. For example, the model predicts the existence of four grain refinement transitions, three of which were observed experimentally. Here the grain refinements in as-solidified Fe–Co alloys were interpreted using the above model. The basic underlying assumption of the above model is that remelting of the dendrite trunks is driven both by capillary forces and by the supersaturation inside the trunk, which becomes important at high undercooling [17]. The fragmentation can be evaluated by adopting a parameter S, the so-called dimensionless measurement of the relative contribution from the two aforementioned driving forces [17],
4.2. The second grain refinement S¼ So far, two kinds of mechanisms for the second grain refinement occurring at high undercooling are favored. The first one is dendrite remelting of the primary dendrites [3], and the second one is recrystallization occurring in the dendrite fragments. As for recrystallization mechanism, Liu et al. [9] deemed that the second grain refinement in DD3 superalloy can be attributed to large stresses originating from lattice deformation and fluid flow induced by solidification shrinkage due to rapid solidification, which results in dendrite distortion, disintegration and recrystallization. Analogously, Li et al. [8] considered that the second grain refinement in Ni–Cu alloy results from the stress caused by the impeded solidification contraction in rapid solidification, which leads to fragmentation and recrystallization of the dendrites. As a fact, dislocations and twins that are indications of recrystallized microstructure were not found in the as-solidified structures of Fe–Co alloy. Furthermore, the average grain diameter was comparable to the dendrite trunk radius, i.e. the dendrite side-branch spacing, so the second grain refinement possibly results from remelting of the primary dendrites rather than recrystallization. 4.3. Comparison with a dendrite break-up model Based on previous work by Jackson et al. [12], a model was proposed for dendrite fragmentation, which is based on the morphological instability of a solid cylinder embedded in its melt leading to a fragmentation of the cylinder into spheres [13]. The driving force for this process is the reduction of the solid–liquid interfacial area. According to this model, the critical transitional undercooling could be determined by comparing two times: the time for dendrite break-up by Rayleigh instability Dtbu and
153
Gc R Ds R , C 0 ð1 kE Þ Dl d c0
(1)
where Gc is the concentration gradient which is negative because the concentration decreases outward from the trunk axis, and d c0 , the chemical capillary length, can be expressed as d c0
G . jml jð1 kE Þc0
(2)
According to Ref. [17], fragmentation is dominated by surface tension and supersaturation inside the trunk, for S51 and Sb1, respectively. On this basis, the prediction in this case for Dtbu (for S51) can be expressed as jml jc0 ð1 kE Þ Dl 3 RðDT Þ3 , (3) 1þ Dtbu ðDTÞ 2 d 0 DT DH f =C p DT where Dl and Ds denote the solute diffusivities in the liquid and solid phase, respectively, DT the thermal diffusivity in the liquid, ml the equilibrium liquidus slope, kE the equilibrium partition coefficient, DHf the heat of fusion, Cp the specific heat at constant pressure, c0 the solute concentration, and d0 ( ¼ Cp/DHf) the capillary length with G the Gibbs–Thomson coefficient. According to Schwarz’s model [18], the trunk radius R(DT) is correlated to the dendrite tip radius, Rtip(DT), via a proportionality constant, z ¼ RðDTÞ=Rtip ðDTÞ 20. This constant is determined by taking the ratio of the trunk radius, measured from micrographs of solidified samples, to the calculated tip radius at the same undercooling. Applying the physical parameter data of Fe70Co30 alloy (see Table 1), the theoretical dendrite tip radius R(DT), as a function of undercooling, was calculated using BCT model [19]. The calculated Dtbu and Dtpl as a function of undercooling are shown in Fig. 3. Three intersection points between Dtbu and Dtpl were observed, indicating that two
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Table 1 Materials parameters of Fe70Co30 used in the calculation of the break-up time Parameter
Dimension
Value
Heat of fusion (DHf) Specific heat (Cp) Liquidus temperature (Tl) Liquidus slope (ml) Diffusion coefficient (Dc) Thermal diffusivity (DT) Equilibrium partition coeffcient (kE) Gibbs–Thomson coefficient (G)
J/mol J/mol K K K/at% m2/s m2/s
15 608 38.4 1765 1.2 4.4 109 2.4 106 0.73 3.7 107
km
Fig. 4. Undercooling contributions vs initial undercooling T.
Fig. 3. Calculated dendrite break-up time Dtbu (thick solid line) and plateau time Dtpl (thin solid line) as a function of undercooling.
grain refinements occur, i.e. the first one occurs within 20 KoDTexpo30 K, and the second one if DTexp4175 K. Basically speaking, this is compatible with the theoretical expectation, i.e. two grain refinements occur at both low and high undercoolings. For the second grain refinement, good agreement was obtained between the theoretical expectation and the experimental result, i.e. DT exp ¼ 175 KDT 5 ¼ 183 K. For the first grain refinement, however, only the initiating undercooling can be predicted using the above model, i.e. DT exp ¼ 20 KDT 1 ¼ 22 K, whereas large deviation remains for the ending undercooling (i.e. DT exp ¼ 30 K DT 2 ¼ 87 K). According to the BCT model [19], the total undercooling at the dendrite tip consists of four contributions, DT ¼ DT l þ DT c þ DT r þ DT k ,
(4)
where DTt, DTc, DTr, and DTk are the thermal, solutal, curvature, and kinetic undercooling, respectively. With increasing DT, the variation of the relative contributions of Tt and DTc to DT reflected that solutal diffusion-controlled growth may give way to thermal diffusion-controlled
growth. As shown in Fig. 4, solutal diffusion predominates if DTo20 K, but it is progressively replaced by thermal diffusion with DT, i.e. the cross-point of DTt and DTc (DT ¼ 25 K) corresponds to the transition from solutal diffusion-controlled growth to thermal diffusion-controlled growth, see Fig. 4. It is then concluded that the effect of solutal diffusion becomes negligible after DT ¼ 25 K according to the BCT model calculation. From Eq. (3), Dtbu is dependent on Rtip(DT) calculated using BCT model, so the regime for the first grain refinement, 20 KoDTexpo30 K (see Fig. 3), was deduced, as compatible with the above conclusion from Fig. 4. As shown in Fig. 1, however, the first granular crystals hold within 22 KoDTo87 K, which implies that the effect of solutal diffusion is still inevitable wherein. So the conclusion that the effect of solutal diffusion becomes negligible after DT ¼ 25 K drawn from BCT model calculation (see Fig. 4) is not physically realistic. On this basis, further considering the effect of solutal diffusion must enlarge the regime for the first grain refinement (see Fig. 3). This is why large deviation remains for the ending undercooling (i.e. DT exp ¼ 30 K DT 2 ¼ 87 K) for the first grain refinement. Unfortunately, only a qualitative interpretation is given here. Anyway, a quantitative explanation is essential for a more detailed investigation on the occurring phenomenon. 5. Conclusion Analogous to other single-phase alloys such as Ni–Cu and DD3 superalloy, two grain refinements were observed in the as-solidified Fe70Co30 alloy melt subjected to undercoolings below a critical value. The first grain refinement occurs within 22 KoDTo87 K, and the second one if DT4183 K. Applying a dendrite break-up model (i.e. on the basis of morphological instability) in combination
ARTICLE IN PRESS N. Liu et al. / Physica B 387 (2007) 151–155
with the BCT model calculation, a theoretical description for the observed grain refinements was given. Both grain refinements are concluded to be caused by dendrite remelting. Good agreement between theoretical expectation and experimental result was found for the second grain refinement, i.e. DT exp ¼ 175 KDT 5 ¼ 183 K. As for the first grain refinement, only the initiating undercooling can be predicted using the above model, i.e. DT exp ¼ 20 KDT 1 ¼ 2 K, whereas large deviation remains for the ending undercooling, i.e. DT exp ¼ 30 K DT 2 ¼ 87 K. This can be ascribed to the fact that the effect of solutal diffusion was deduced to be negligible for DT425 K in BCT model calculation. Acknowledgments The authors are grateful to the financial support of the Natural Science Foundation of China (Grant nos. 50395103 and 50501020). References [1] J.L. Walker, in: G.R.S. Pierre (Ed.), Physical of Process Metallurgy, Part 2, AIME, Interscience, New York, 1961, p. 845. [2] K.A. Jackson, J.D. Hunt, D.R. Uhlmann, J. Mater. Sci. Lett. 245 (1969) 407.
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[3] T.Z. Kattamis, M.C. Flemings, Trans. TMS-AIME 236 (1966) 1523. [4] A.M. Mullis, R.F. Cochrane, J. Appl. Phys. 82 (1997) 3783. [5] R. Willnecker, D.M. Herlach, B. Feuerbacher, Appl. Phys. Lett. 56 (1990) 324. [6] R. Hermann, W. Lo¨ser, G. Lindenkreuz, A. Diefenbach, W. Zahnow, W. Dreier, Th. Volkmann, D. Herlach, Mater. Sci. Eng. A 375–377 (2004) 507. [7] D.M. Herlach, K. Eckler, A. Karma, M. Schwarz, Mater. Sci. Eng. A 304–306 (2001) 20. [8] J.F. Li, Y.C. Liu, Y.L. Lu, G.C. Yang, Y.H. Zhou, J. Cryst. Growth 192 (1998) 462. [9] L. Feng, Y. Gencang, G. Xuefeng, Mater. Sci. Eng. A 311 (2001) 54. [10] J. Li, G. Yang, Y. Zhou, Mater. Res. Bull. 33 (1998) 141. [11] N. Liu, G. Yang, F. Liu, Y. Chen, Y. Zhou. Mater. Charact., in press [12] K.A. Jackson, J.D. Hunt, D.R. Uhlmann, T.P. Seward, Trans. TMS AIME 236 (1966) 149. [13] M. Schwarz, A. Karma, K. Eckler, D.M. Herlach, Phys. Rev. Lett. 73 (1994) 1380. [14] A. Karma, Int. J. Non-equilib. Proc. 11 (1998) 201. [15] A.F. Norman, K. Eckler, A. Zambon, F. Gae`rtner, S.A. Moir, E. Ramous, D.M. Herlach, A.L. Greer, Acta mater 46 (10) (1998) 3355–3370. [16] K. Eckler, M. Schwarz, A. Karma, D.M. Herlach, Mater. Sci. Forum 45 (1996) 215. [17] A. Karma, Int. J. Non-Equilib. Process. 11 (1998) 201. [18] M. Schwarz, A. Karma, K. Eckler, D.M. Herlach, Phys. Rev. Lett. 73 (1994) 1380. [19] W.J. Boettinger, S.R. Coriell, R. Trivedi, in: R. Mehrabian, P.A. Parrish (Eds.), Rapid Solidification Processing Principles and Technologies IV, Claitors, Baton Rouge LA, 1988, p. 13.